Stripes in the extended $t-t^\prime$ Hubbard model: A Variational Monte Carlo analysis

By using variational quantum Monte Carlo techniques, we investigate the instauration of stripes (i.e., charge and spin inhomogeneities) in the Hubbard model on the square lattice at hole doping delta = 1/8, with both nearest- (t) and next-nearest-neighbor hopping (t'). Stripes with different wavelengths lambda (denoting the periodicity of the charge inhomogeneity) and character (bond- or site-centered) are stabilized for sufficiently large values of the electron-electron interaction U/t. The general trend is that lambda increases going from negative to positive values of t'/t and decreases by increasing U/t. In particular, the lambda = 8 stripe obtained for t' = 0 and U/t = 8 [L.F. Tocchio, A. Montorsi, and F. Becca, SciPost Phys. 7, 21 (2019)] shrinks to lambda = 6 for U/t greater than or similar to 10. For t'/t < 0, the stripe with lambda = 5 is found to be remarkably stable, while for t'/t > 0, stripes with wavelength lambda = 12 and lambda = 16 are also obtained. In all these cases, pair-pair correlations are highly suppressed with respect to the uniform state (obtained for large values of vertical bar t'/t vertical bar), suggesting that striped states are not superconducting at delta = 1/8.